 I'm switching immediately to the next presentation and in this case, it's a paper by Pia Paolo Benigno together with Gianluca Benigno. Pia Paolo is from the University of Bern and he's presenting also a topic that's very high on the minds of many policy makers for the moment and that's managing monetary policy normalization and particularly on the sequencing given that we have a variety of tools that central banks deploy, how do you manage this monetary policy normalization? Let's go ahead Pia Paolo. Yes, thank you very much Isabel and for the invitation to this conference. It's a pleasure to be here so let me share my presentation. So as you say it is a job work with Gianluca Benigno and I would say it's, as you mentioned you know it's a quite relevant topic right now because after having expanded balance sheet and pursue zero interest rate policies central bank are now concerned about normalization and on top of this normalization there are also other shops which are in some way asking for more for a higher speed of rising rates and eventually reducing the balance sheets. So here we are basically more concerned about you know standard approach in which you enter a liquidity trap and then the shock banishes and then you ask how you exit the liquidity trap but both from the case of interest rate policy and balance sheet. I have to say that there is no much literature on in general the pace and the timing of quantitative tightening in combination with the zero lower bound in the lift off of the policy rate whether you know quantitative tightening should come early then the lift off or later or at which pace so this paper is going to study this and obviously it's going to be a model in which balance sheet policy are relevant. So what we do we study an economy in a liquidity trap in which reserves are a relevant tool of policy on top of the interest rate policy and there we characterize the managing of QE and QT together with zero lower bound policy. So what are the results that I'm going to stress so under optimal policy reserve should increase lately in a liquidity trap so not shouldn't be the early use in the trap but it should pick up later and before the lift off of the policy rate they should reach the peak and then we draw at the slow pace and this is the result under standard calibration then we're going to have a case in which there are higher spreads in money markets before entering into the liquidity trap those conditions require a larger QE stimulus and a similar withdrawal with respect to the previous case when instead central bank are more concerned for output stabilization again there is a request for a larger QE and a faster QT. So let me present the framework and this is going to be what I say what I call a general framework for monetary policy analysis because it's going in some way to nest as a particular case the new xylian eukonation framework. The characteristic of the new xylian eukonation framework is that central bank can control inflation and output by just using one tool the policy rate which is usually in this model the interest rate on reserves and in general reserves although a policy tool are irrelevant for inflation and output. Instead the more general framework that we develop in this paper gives an independent role to reserve as a tool for controlling inflation and output and there are some features of the transmission mechanism that I'm going first to describe in words and then with a simple example. So the main characteristic is that the consumption saving choices so usually the Euler equation that characterizes these choices depend on the interest rate on a liquid asset and which is not the policy rate and the demand of liquid asset by the household depends instead of the liquidity spread between liquid and illiquid securities. Here it comes the role of the central bank because the central bank and the treasury are the supplier of liquid asset which are backed by reserves in the case of for example deposits of commercial bank and they also determine through the interest rate on reserve the interest rate on liquid asset. So by controlling the quantity of reserve and the interest rate on liquid asset then the central bank can have an influence on the demand of liquid asset and influence also the interest rate on illiquid asset. So this is the mechanism and let me describe it through detailing what I said through some equation. So here we have a Euler equation which relates the consumption today to consumption tomorrow but the relevant interest rate here is what we call the natural nominal rate of interest which doesn't coincide with the policy rate. That's the rate on illiquid asset. Then the demand of liquid securities you can see here depends on the liquidity premium in a negative way because this is the marginal utility that you get from liquid securities and it depends on the natural nominal rate of interest which is the interest rate on illiquid securities and the interest rate let's say on deposit which are liquid securities. So what is happening here is that the central bank doesn't enter into any of these equations so it works through the banking sectors in which the deposit rate is going in equilibrium to be related to the policy rate. So by controlling the policy rate the central bank can in some way control the deposit rate and then act to control the natural nominal rate of interest which affects the consumption-savvy choices. So when I combine this equation I actually get a relation between this rate which affects the consumption-savvy choices IB and the policy rate IR. So the relation you see is not direct is proportional but it's not one-to-one because there is a term which is going to depend on the liquidity premium association but what is more important is that to control the rate IB you need to specify both the interest rate on reserve and the quantity of reserve which is going to affect the liquidity to the column. So this is the new channel and when for example this marginal utility of Q is BQ is 0 then you are back to the new Keynesian model. So this is going to be a model in which the two tools interest rate on reserves and quantity of reserves are going to influence consumption-savvy choices and so they are relevant tools. Okay so let me skip the literature review and go to present the model so there's going to be a very simple in this paper but we have a more complicated framework in another companion paper banking model in which intermediaries live for two periods and are subject to limited liability constraints which here is quite irrelevant because these intermediaries do not face any any any risk in their balance sheet. So they can basically invest in reserve and in illiquid assets which are risk-free they issue deposit and they have equity and they are subject to some collateral can be or regulatory requirement can be implicit or explicit form and which say that reserve should be a large should be a fraction of deposit with this row which is between zero and one. So given this setup profits of intermediary are going to depend on their return on their asset which are these illiquid assets that have the interest rate IB which is the one I showed you before and the return on reserve which is the interest rate on reserves and at the same time they pay their liability with the interest rate B so where is the limited liability constraints it's just asked that the profits of intermediary should be non-negative. So in this model intermediary are maximizer maximize strengths subject to the limited liability constraints and to the collateral requirements and this simple framework deliver a simple result so the one I showed you before so that the interest rate on deposit is going to be a weighted average of the interest rate on reserve and on this natural nominal rate of interest which is the interest rate on illiquid debt debt with illiquid characteristics so that doesn't provide liquidity to agent. While the demand of equity in this model just comes from the collateral constraints they shouldn't be negative otherwise sorry the limited liability constraints otherwise profits would be negative. So what is interesting is that there are conditions in which the Nubi-Xenian framework is nested through this banking model one is when reserves are very abundant so that the collateral constraints doesn't bind so in that case all these interest rates are the same and we have the traditional transmission mechanism in which reserves are irrelevant for inflation and output. The other case is the one in which rho is equal to zero so when you don't need reserve to satisfy collateral constraints whether this is imposed by the government or is something in the banking sector and in this case all interest rates are also equalizes so in some way reserves also in this case do not offer any non-pecuniary service to the banking sector. However you know a case which is interesting and we are going to analyze is when rho is equal to one then it's true in this case that the interest rate on deposit is equal to debt on illiquid asset on reserves but those rates may be lower than the interest rate on illiquid asset so here it's a case also that is going to nest in some way a case in which central bank issued digital currency for example in some form like deposit of household held at the central bank. Okay so let's go to the other part of the model households that get utility from consumption and liquidity services and in particular the liquidity services are provided by two type of securities treasury notes and deposit and both are substituted so they get the same interest rate ITD which is going to be determined in equilibrium. Agents can also borrow and lend in liquid private securities which are BT and they have a different rate which is the one I was mentioning before the natural nominatorate of interest ITD. So optimality condition from these households with standard separable preference between consumption and liquidity services so you get the Euler equation which is the same I show you before but in a stochastic environment and then the demand of liquidity which is going to equates the marginal rate of substitution between liquidity and the consumption to the spread between illiquid asset and liquid asset so this is going to be the queue demand we had before. Agents also supply labor in this model and the firm use labor to produce good and a subject to the standard model of price rigidity as in the New Keynesian framework. Here you know we're going to integrate treasury and central bank for simplicity and we basically assume that they share same characteristic with respect to reserve a depth so the overall issuance of reserves and debt securities by the treasury is given by the previous level of debt and the previous level of reserves and their different interest rate because in principle those can have different interest rate and taxes are a way to reduce these overall liability of the government. Contrary to the New Keynesian framework the tax policy is going to be very critical for the determination of prices and for the relevance of reserve policy so I'm going to present the model in a simple way in a log linear approximation so the model is going to be consistent with the same aggregate supply equation as in the New Keynesian model which inflation depend on output gap and expected future inflation. What is more complicated here is the aggregate demand block. Here is the approximation of the Hewler equation and that would be enough if these were the policy rate but is not the policy rate so you need the transmission mechanism there and here we have two other elements we have the demand of liquidity which depends on outputs and on the spread between liquid and in liquid asset and we have the banking relation between interest rate on money market which is going to say that the natural nominate rate of interest depends on the interest rate on reserves and on the spread between liquid and in liquid asset so not again that these view parameters is quite important because it indicates the degree of association of liquidity in the economy when v is equal to zero we are in a fully associated economy with liquidity and then all the interest rates are going to be equalized and can move in the same way so all money market rates are going to be in the same direction and this is going to nest exactly the New Keynesian framework again on top of the other two elements I was discussing before in the banking sector. Now what is interesting is that this three equation can be combined to deliver a new aggregate demand equation which is similar to what we think is the standard demand equation in New Keynesian model but there's some features which are interesting here so the first feature is that here in front of this future output we have a coefficient which is less than one so basically when you iterate forward this equation this equation is going to give you less importance of forward guidance in influencing the current demand. The second important element here is the influence of liquidity on demand so higher liquidity is push aggregate demand and that's how reserves are going to matter in this model and here we have the policy rate so you see the combination of the two policies entering through the aggregate demand equation. So we make an analysis of optimal policy and I'm going to present a case which gives a sort of trivial answer and then we're going to have a more complicated case and the case with a trivial let's say straightforward answer is when lump sum taxes are available and as I say before taxes becomes very relevant in this context. So the objective function which is a second order approximation of the welfare of the consumer in this model is going to have a standard form in which central bank should care about the output gap and inflation with respect to the target but there's also a new element which is the distance between the liquidity in the system and the association level of liquidity. So when qt is equal to q star then association is rich in the economy and liquidity is at the first best. Now when you look at this problem and you make an analysis of optimal policy as a very straightforward conclusion which is that basically there is no trade-off. So optimal policy should reach should liquidity should be such to reach the full association and then inflation and outputs should be stabilized to the target and this happens also if you are this if you have shocks that bring you the economy the zero-overbound so what I mean it means that the liquidity policy is to reach association while here there is going to be a trade-off you know the standard trade-off in stabilizing inflation and output because of the presence of the zero-overbound but the model doesn't change the conclusion of the standard literature in this case. There is a caveat things are going to change a little bit but not much when preferences are not separable between consumption and liquidity but in general you know even this framework can say something on liquidity policy and say that basically if they are not set optimally at the beginning of the liquidity trap then increasing reserves lowers the stay at the zero-overbound so and that's the only case in which in this type of analysis they would matter. So let me show you this case here we have a different rule but just focus on this line the Qt equal to zero so that would be the case the standard model in which you have a shock bringing you to the liquidity trap you see interest rate staying 13 quarters here sorry 15 quarters to the zero-overbound and then going up you see inflation going down and then up and then you see the output gap going down and then up so that's the standard optimal response of policy to condition then bring the economy to the zero-overbound now if Qt is not set optimally then you have this response now if you rise Qt then you're going to see you see that is going to lower so if liquidity rise then you're going to lower the stay at the zero-overbound so obviously if you start from condition in which liquidity is not uh it doesn't reach cessation then if you have a shock they bring the economy to the liquidity trap you increase liquidity into the system then it's going to stimulate aggregate demand and it's going to require lower stay at the zero-overbound so it's actually offsetting the shocks that bring you at the zero-overbound but as I say this is I think the least interesting case so what is more interesting is when there are distortionary taxes and here we make a simplifying assumption which is going to say that the liquidity constraint just say that to back the positive unit reserve and in this case the interest rate on deposit is equal exactly to the interest rate on reserves now what is relevant when taxes are distortionary it becomes the intertemporal resource constraints of the economy which is going to imply that Q which is going to be the sum of reserves and treasury debt so the the value of Q at time t uh so this is the outstanding debt divided prices should be backed should be equal to more than backed by the present discounted value of the taxes that the government live by here in a distortionary way so taxes are proportional to income then there is still an exogenous transfer which is helpful in our model and you know you can have some resources also coming from the fact that Q have liquidity properties and in this way the interest rate on R can be lower than B this gives some let's say rents to the government in a way to back the level of debt so this constraints becomes a relevant constraints for the optimal policy problem when you have distortionary taxes usually when you have lump sum taxes this constraint is no longer is is let's say residual you can use lump sum taxes to fulfill it but with distortionary taxes this becomes relevant and therefore the optimal supply of liquidity has to consider these constraints so when you analyze the optimal supply of liquidity in the economy Q in the steady state you find that it does not imply any more full cessation so basically in this model with distortionary taxes the optimal steady state policy of liquidity is not to satiate the economy but to keep actually some uh spread in the money market and we can see from this condition in which the marginal utility of liquidity is positive because these fee are non-negative and lagrange multiplier and this second derivative is negative because of the shape that you want to have for the liquidity demand function close to the association so what is important is that in the previous case when we start five minutes there's five minutes left when you have lump sum taxes available these parameters is zero so the optimal policy is to the optimal steady state is to have a full cessation of liquidity so given this setup the model becomes a bit complicated but not much the loss function is still similar as before but you have an additional terms again which characterize the deviation of liquidity from this optimistically the state I described before the aggregate supply equation change because these taxes are now distortionary so you see equation number four uh equation number five is doesn't does not change and you can see that you know you have the less than one coefficient with respect to future output and then you have the liquidity that affect demand so this is the aggregate demand equation and the problem is also subject to the inter-temporal budget constraints I showed you before in a log linear approximation now we make the analysis such that when this variable FT year that is called the fiscal stress is zero then you can achieve a full stabilization of output inflation and QT and this is compatible with the inter-temporal budget constraints of the government but obviously you know when the zero overbound is non-binding but when the zero overbound is binding even if FT is going to be zero you're going to have a trade-off and that's what is going to be analyzed here okay so what I'm going to do is I'm going to compare the optimal policy here with sub-optimal policy and those are two class of sub-optimal policy let me just tell you in words first type of policy is a it's a it's a only one policy but in which tax policy is doing something and monetary policy is doing something so monetary policies try to fix inflation on the target if it can if it cannot it has to set the policy rate to zero so it's a very strict inflation targeting policy and the fiscal authority doesn't vary the tax rate okay so what you get is a standard result in which the sub-optimal policy are really sub-optimal and here you can see that the optimal policy when you look at the interest rate asks you to stay longer at the zero lower bound so this is the standard result in the literature now what is interesting is what policy is asking in terms of liquidity so the dash blue line is the policy in is the outcome in the sub-optimal policy and the dark line is the straight line is the liquidity policy under optimal policy so you can see actually that you don't want to increase liquidity but you only do leisure in the trap and then just before the lift off of the policy rate you start to withdraw liquidity and you withdraw very slowly okay now the other characteristic of optimal policy which is in line with other studies is that you rise the taxes at the beginning and you lower that when the shock disappears and that's because you want to push inflation up you can see that after the optimal policy inflation is really stabilized here okay let me show you something interesting in the few times that I have now what we find under this optimal policy is that okay if we shut down liquidity and say okay central bank doesn't use liquidity then everything doesn't change much so it seems that there is no much role of reserves in affecting the enter and the exit of the liquidity trap we ask what is going to happen if money markets spread are higher so if money markets spread are higher this is going to rise this parameter V in the demand equation and possibly this is giving much more role to QT in affecting aggregate demand and the calibration we do here is to have this V at four percent which are spreads that we have seen just before the financial crisis now when we compare the optimal policy with a constant liquidity policy in this case which is the red line and the black line we see that basically they imply the same lift off of the policy rate so liquidity and non-liquidity doesn't change much the exit the time you stay at the zero lower bound what is happening with larger credit spread that you see now comparing the blue line and the dark line here with real liquidity is that you increase liquidity more before you were not increasing liquidity but now you increase liquidity more you pick just before the lift off of the policy rate and then you go down and then very very slowly last figure which is interesting I guess is when central bank cares more about how to go this kind of model new kinesia model gives too much weight to inflation with respect to output and indeed all the figure before you don't say okay yes we try to stabilize inflation more than output now we consider a case in which you try to give more weight to the output gap objective in the stabilization problem and here things are very interesting so when we compare optimal policy the sub-optimal policy with the blue line and the liquidity and the constant liquidity policy which you don't use a balance sheet policy at all now you can see that liquidity pickups a lot so you increase liquidity a lot here and before the trap but then you withdraw it very very fast and now the liquidity policy by comparing the optimal policy and the constant liquidity policy as an effect because if you use liquidity you don't stay so much long at the zero but you stay you go out early only if you don't use liquidity you stay longer okay but you see that you start to withdraw liquidity early and then at the time in which the policy rate is normalized also liquidity start to be normalized so the intuition here is the following when you give a lot of weight to output gap and you can see here that you stabilize output during the shock actually and you let a bit inflation to vary more during the shock then you want to use a lot the liquidity policy unless the interest rate policy while instead when you care more about inflation even during the trap so you try to stabilize inflation well at the 2 percent target even during the trap then there you don't want to use much liquidity policy and you want to use actually more the tax policy and actually you see here that the tax policy goes completely on the other side that you lower taxes at the beginning of the trap and you rise taxes at the end of the trap so this is actually the way you boost a bit inflation at the beginning of the trap and then you lower it at the end of the trap okay so let me conclude by saying that this is a presented what I hope is a general framework to understand the effectiveness of reserves as an additional tool for monetary policymaking in which next under some particular condition the new Canadian framework and the determination of inflation is a function of three important policy tool tax reserves and interest rate and obviously it's not a conclusive analysis on the pace and the speed and the timing of QE and QT but at least you know I think he provides some elements for discussion thank you very much thank you very much Pia Paolo I immediately pass the forum to Elisa Rubbo from the University of Chicago who has prepared a discussion of the paper all right thank you very much for inviting me to discuss this very interesting paper all right so there is a large literature of New Canadian models that consider unconventional policies to address the euro or bond so as your fellow was saying there is a large set of policies that received a lot of attention such as forward guidance government spending or tax policy but the novelty of this paper is to consider instead the role of reserve management and liquidity management so the authors make a simple argument for how this works essentially they argue that in the real word there is not just one interest rate on safe assets there is actually two one is the the nominal rate faced by households in their consumption saving decisions like the euro equation and the other is the reserve rate and typically the reserve rate is going to be smaller than the the actual interest rate faced by households and the reserve rate is what the central bank has control over and increasing the amount of reserve in the economy is going to lower the gap to decrease the gap between the nominal rate faced by households and the reserve rate and so in particular when the reserve rate is stuck at zero increasing the amount of reserve is very useful because it is just going to lower the the nominal rate that goes into the euro equation and this has the desired cumulative effect on the economy so this is a great benefit it comes at a cost which is that essentially increasing the amount of reserves increases the government balance sheet and this is finance for taxation and taxation is distortionary so this is the argument in a nutshell I really like the positive model of reserve management that this paper provides so in this discussion I will briefly review the a bit more in detail the argument of the model and then I will mostly focus my comments on the normative implications of the model so I think the normative implications are also kind of the more innovative aspect of the paper in the sense that we have like not very many but some models of central bank balance sheet and reserve management such as the work of Monica Piazzia-Martizan either but I think this work doesn't really focus on the normative implication of optimal reserve management so this is really the the new aspect of this paper and I think the paper provides a great baseline to think about optimal policy but I would encourage the others to think a bit deeper about a few questions that I will outline in the discussion in particular as they point out the role of tax taxation and like the management of taxation is crucial and it's jointly determined with the reserve policy so I will discuss a bit like how this could potentially change depending on the tax instruments that are available and then I will try and discuss a bit more the composition of the central bank assets portfolio so in the paper essentially the central bank is buying government bonds but in practice central banks might buy other assets like a richer set of assets and I think this really interacts with the cost and benefits of fishing liquidity all right so let me jump through the model I will not show many questions I will just like provide like a schematic summary of the argument so in this word there are going to be two main agents that determine the asset market story the private banks and the government and by government I'm going to mean like the like the the joint set of like fiscal authority in the central bank so in the balance sheet of private banks the assets are preserved and private bonds so essentially banks are lending to the central bank through reserves and to the consumers through the private bonds and on the liability banks are financed through deposits and equity that are both both end up being held by the consumers the government balance sheet has on the asset side stocks revenues and tenured from well the lower interest rate they pay on reserves compared to the market interest rate and on their liabilities they would have the reserves that is like how they get funded for the central bank and government bonds all right and the two liquid assets that the consumers can hold are the government bonds and the deposits so importantly we will show that like the author showed that by changing the composition of the government's liabilities the government actually can change the amount of liquid assets that are available to the consumer in a way that I would that's the pure pilot statement I will review in a second but the important thing in the model is that there are going to be meaningful spreads between the return on these assets so there is some utility benefit from holding liquid assets which determines the spread between the private issued bond bonds rate that is ID and the return on deposits so essentially deposits are liquid so they pay a lower return moreover there is going to be in general spread between the deposit rate and the reserve rate because banks are constrained to back deposits with reserves all right so great all right so the government in this in this setting has two ways of increasing the the amount of liquidity one is to change the composition of the government liabilities and the other is to increase the size of the government balance sheet all right so thinking of thinking again on the thinking back on the previous slide why does changing the composition of liabilities affect the amount of reserves in the economy well essentially to the extent that deposits can grow more than one-on-one with reserves increasing the shift in the composition of the balance sheet away from government bonds and the worth reserve is going to increase the capacity of banks to generate deposits and deposits are liquid assets so this is going to increase the amount of liquidity in the economy but this channel works only if the the reserves so the deposits need not be back to one-for-one with reserves as long as they need to be back one-for-one then the only way that the central bank has to increase the amount of liquid assets in the economy is to just increase the size of its balance sheet and this can be done either for reserves or government bonds but the problem of doing this is that essentially the central bank is going to have to pay more interest because it's borrowing more and paying interest require raising taxes and so taxes are distortionary so this has a cost so basically increasing the amount of liquidity has a cost so essentially we have a meaningful trade off at this point in the choice of the optimal amount of liquidity and the others show that there is a different trade-off in steady-states and in a case where there is a ZLB so in steady-states the trade-off is between the utility benefits of increasing the amount of liquidity and the cost of present liquidity coming from distortionary taxation as a result of the trade-off in steady-states liquidity demand will not be stated. When the ZLB binds, the others show that there is an incentive to deviate from the optimal liquidity tax trade-off and in particular increasing liquidity as we explained before helps lowering the minimum for nominal rate for households and therefore it can mitigate the fall of output and prices at the ZLB for a given promised future path of these variables all right and the nice the very nice thing is the paper is that the others show that their loss function that described welfare in this paper is very similar in a way to the to the traditional nuke angel loss function it's like a quadratic loss function that depends on output and inflation with this new like output gap and inflation gap with this new part gap that puts out that is the liquidity gap right so here I have a few comments about the way that they think about optimal policy so the others show that there is a digital dynamic that is an interdependence between reserve taxes and output and inflation and so the timing of the reserve accumulation matters and it depends on the weight of inflation versus output one benchmark that they would have liked to see to understand a bit better where these dynamics come from is actually a benchmark where there is no active liquidity or tax management and my understanding of all the policies that were shown in the paper is that they either have active liquidity management or active tax management but for me the benchmark in this kind of ZLB literature is for example the learning papers where there is no active liquidity or tax management but the central bank at the same time is realizing the value of like promising like higher future output or inflation so I think like either the central bank was super naive and it didn't even do this last thing of like thinking of like forward guidance or it was like sophisticated enough that it would consider some active liquidity or tax management but I think the there was a bit of dismissing comparison that I thought would be actually useful and another point that I think is very important actually is that the assumptions about the tax instruments matter a lot for what the optimal policy is going to look like so in the paper the only tax instrument is the an output tax on like producers or consumers but there is no way to stop it so essentially raising this tax is going to create inflation and it's going to lower the real wage and so depress labor supply so increasing inflation is good but depressing labor supply is bad and so we see immediately that if the central bank cares a lot about inflation stabilizing inflation then it wants this tax because there is deflation so we want to counteract that but if it cares about output then it actually doesn't want much of this tax and I think that is kind of like key like that the use or not use of this instrument is kind of key for them there is the result about how the central bank is using results in the model another and I'll just say show this with a couple graphs so we see that here the central bank cares about inflation so it actually is raising the tax so it simulates it creates inflation and it lets the output gap fall but as soon as the central bank cares about the output oh okay sorry I messed up actually I put the same time the same the I put twice the same figure sorry about that but anyway in the other figure the output gap is very stable and actually the tax goes down and then up so it's like the opposite path of the tax apology next up but anyway just to make the point that I think the the tax rate is like it's kind of the different evolution of the tax rate is kind of key to the to the results and that also must interfere with the reserve determination so I think that's the point to clarify and another reason why I think the taxation part is important is that we know that if we had instead of just the output tax also with wage subsidy then we would be able to basically stabilize the ZLB just with the tax policy so I think this is a point that the authors should address they could see maybe it's not realistic to assume that we can manage taxes so well although in their model there is quite a bit of active tax management so I think this is just a point like I think it's a pushback that the authors might encounter and I think it would be important to address all right so let me basically conclude this is my last slide with a bit of a broader discussion of the trade-off behind issuing liquidity so I think in a large set of models as increased like especially at the Virginia's agents model which is different from the representative agent case in this paper increasing the amounts of government debt so increasing the amounts of liquidity is a way to transfer resources to foreign constrained agents and I think it is in output so that could be because low MPC savers essentially can borrow okay lend to IMPC borrowers buy buying government bonds and like the bonds pay like it rebates to everyone and another another role of having liquidity is that it permits the channel resources from unproductive savers to productive entrepreneurs so in both cases I think it might be important to model a bit more in detail the sources of the liquidity benefit and especially I think this is important if we consider that a scenario where the central bank is not just buying government bonds but it's directly buying private assets so I think this is important in changing the trade-off in the model because essentially the needs to raise taxes was coming from an expansion of the amount of government borrowing in the model but if the government is just buying private assets and actually making a return like making money out of those private assets because they are paying an interest rate higher than the reserve rate at which the government is borrowing at then the government is actually giving a rebate it's not it's not in need of raising taxes so I think the composition of the central bank asset portfolio can be very important in changing both the benefits and the cost of additional liquidity of course this kind of requires taking a stance like do we think that the central bank is kind of stepping in where credit income is constrained a bit like like Gertler and Karadi or do we think that the central bank is just really trying to offset the ZLBA so I think these are all considerations that I would have liked to see a bit discuss a bit more in the paper all right so to conclude I think this paper provides a great work of course models of reserve management and it does a really good job at highlighting the the complicated connections between reserve policy interest rates and the government budget and taxation the normative analysis is a great baseline I wonder if discussion rate taxation is really the main cost that we view to the issuance of liquidity I think the connection with tax instruments should be dealt a bit in a more in depth way and also the allocative role of liquidity and the composition of the central bank portfolio and another aspect that it's totally beyond this scope of this paper but might be interesting and related is the interaction with active financial markets and communication aspects and avoiding paper tantrums and so on so thanks for a great paper it was very for provoking and thank you again for inviting me to discuss thank you very much Elisa I'm getting messages here from the organizers that we're running out of time basically we've exhausted even the whole break time so unfortunately we'll have to break up the session here but I guess you can interact also by actually with Pierre Paolo on the comments and I think it was a lot of interesting food for thought and a very interesting paper so I'm really sorry that I cannot go into more details in the discussion but you know there's a time limit which I've been asked to strictly adhere to here now